2024/09/25 by Munn, Thomas Jack, Riedler, Oskar
#53C35 #53C43 #58E20 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2409.16932
In this note we study (λ,μ)-eigenfamilies on compact Riemannian manifolds when λ= μ. We show that any compact manifold admitting a (λ,λ)-eigenfunction is a mapping torus and that any (λ,λ)-eigenfamily is one dimensional. Additionally, we consider generalised eigenfamilies, which can have higher dimension, and relate these to harmonic Riemannian submersions to a torus.